{
  "id": "1007.4845",
  "version": "v1",
  "published": "2010-07-27T23:25:11.000Z",
  "updated": "2010-07-27T23:25:11.000Z",
  "title": "The Largest Subsemilattices of the Semigroup of Transformations on a Finite Set",
  "authors": [
    "João Araújo",
    "Janusz Konieczny"
  ],
  "comment": "7 pages",
  "categories": [
    "math.GR",
    "math.CO"
  ],
  "abstract": "Let T(X) be the semigroup of full transformations on a finite set X with n elements. We prove that every subsemilattice of T(X) has at most 2^{n-1} elements and that there are precisely n subsemilattices of size exactly 2^{n-1}, each isomorphic to the semilattice of idempotents of the symmetric inverse semigroup on a set with n-1 elements.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-07-27T23:25:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20M20",
      "06A12"
    ],
    "keywords": [
      "finite set",
      "largest subsemilattices",
      "symmetric inverse semigroup",
      "full transformations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1007.4845A"
    }
  }
}